Were children in Second Class allowed to eat with their parents? I saw a thread stating that only full-fare passengers were allowed to eat with their parents, but that was for First Class. What was the deal with Second?

The Laroche family in 2nd Class were traveling on the Titanic specifically because their children (the oldest only 3 years old) would be able to dine with them. They had found that this was not the case on ships of the French Line, which provided separate dining rooms specially for children. And the Laroche's ticket price suggests that the children were travelling at the normal reduced rate (half price).

Most second class families were emigrating, so their travel preparations would have been extremely involved.

I assume you're asking because your characters are going to have to decide to travel at the last moment? If that's the case, I don't see why you couldn't have them book passage at the last moment. I don't know if they would have been seriously gouged on ticket prices, but there was certainly space available.